DRAFTVERSION FEBRUARY 28, 2019 Typeset using LATEX twocolumn style in AASTeX62

A Near-coplanar Stellar Flyby of the Host Star HD 106906

ROBERT J.DE ROSA1, 2 AND PAUL KALAS2, 3

1Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA 94305, USA 2Department of Astronomy, University of California, Berkeley, CA 94720, USA 3SETI Institute, 189 Bernardo Ave., Mountain View, 94043, USA

(Received 2018 December 11; Revised 2019 January 17; Accepted 2019 January 21) Submitted to AJ

ABSTRACT We present an investigation into the kinematics of HD 106906 using the newly released Gaia DR2 catalog to search for close encounters with other members of the Scorpius–Centaurus (Sco–Cen) association. HD 106906 is an eccentric spectroscopic binary that hosts both a large asymmetric debris disk extending out to at least 500 au and a directly imaged planetary-mass companion at a projected separation of 738 au. The cause of the asymmetry in the debris disk and the unusually wide separation of the planet is not currently known. Using a combination of Gaia DR2 astrometry and ground-based radial velocities, we explore the hypothesis that a close encounter with another cluster member within the last 15 Myr is responsible for the present configuration of the system. Out of 461 stars analyzed, we identified two candidate perturbers that had a median closest approach +0.93 +0.90 (CA) distance within 1 pc of HD 106906: HIP 59716 at DCA = 0.65 0.40 pc (tCA = 3.49 1.76 Myr) and +0.18 +0.54 − − − HIP 59721 at DCA = 0.71 0.11 pc (tCA = 2.18 1.04 Myr), with the two stars likely forming a wide physical − − − binary. The trajectories of both stars relative to HD 106906 are almost coplanar with the inner disk (∆θ = +0.9 5◦.4 1.7 and 4◦.2 1.1). These two stars are the best candidates of the currently known members of Sco–Cen ± − for having a dynamically important close encounter with HD 106906, which may have stabilized the of HD 106906 b in the scenario where the planet formed in the inner system and attained high eccentricity by interaction with the central binary.

Keywords: astrometry — and satellites: dynamical evolution and stability — stars: kinematics and dynamics — techniques: radial velocities — stars: individual (HD 106906, HIP 59716, HIP 59721)

1. INTRODUCTION & Davies 2009; Parker & Quanz 2011; Pfalzner et al. 2018), Close encounters by external stellar perturbers have the as well as the observed structure of disks around HD 100453 potential to significantly modify the architecture of plane- (Wagner et al. 2018), HD 141569 (Ardila et al. 2005; Reche tary systems (Laughlin & Adams 1998; Kenyon & Bromley et al. 2008), HD 15115 (Kalas et al. 2007), and β Pictoris 2004). Stars passing very close to our have been (Kalas & Jewitt 1995; Ballering et al. 2016). invoked to explain the formation of the Oort cloud of comets In the case of β Pic, Kalas et al.(2000) and Larwood & (Duncan et al. 1987), comet showers (Hills 1981), the dis- Kalas(2001) explore numerical models of a non-coplanar arXiv:1902.10220v1 [astro-ph.EP] 26 Feb 2019 ruption of the Kuiper Belt (Kobayashi et al. 2005), and the stellar flyby (∆i = 30◦) that qualitatively reproduce the disk asymmetries measured beyond the 200 au projected distant detached of dwarf planets such as 90377 Sedna ∼ (Brown et al. 2004), as well as the hypothetical Planet Nine radius; the northeast disk extension is radially extended and (Bromley & Kenyon 2016). Such close stellar encounters vertically flat whereas the southwest disk extension is radi- have also been invoked to explain the orbital properties of ally truncated and vertically extended (Kalas & Jewitt 1995). extrasolar planets (Zakamska & Tremaine 2004; Malmberg Using astrometry from the Hipparcos catalog, Kalas et al. (2001) identified several candidate perturbers that had a close encounter with the β Pic system in the last 1 Myr that could Corresponding author: Robert J. De Rosa explain the asymmetry. The proximity and large apparent [email protected] motion of β Pic were conducive for this analysis given the 2 DE ROSA &KALAS precision of the measurements available at the time. The or- 1.7 φ = 0.058, BJD = 2457904.48 der of magnitude improvement in the astrometric precision 1.6 of the recently published Gaia DR2 catalog (Gaia Collabo- 1.5 ration et al. 2018) makes it feasible to extend this analysis φ = 0.247, BJD = 2457224.50 to more distant stars that also show evidence of dynamical 1.4 perturbation. 1.3 In this paper we present an investigation into the dynam- φ = 0.517, BJD = 2456794.68 ical history of HD 106906, an F5V (Houk & Cowley 1975) 1.2 member of the 15 Myr-old (Pecaut & Mamajek 2016) Lower 1.1 φ = 0.712, BJD = 2456705.85

Centaurus–Crux subgroup of the Scorpius–Centaurus OB as- Flux +1 Offset (arbitrary. units) 0 sociation (Chen et al. 2011). HD 106906 rose to prominence 0.9 with the discovery of a planetary-mass companion (11 2 ± 6120 6130 6140 6150 6160 6170 6180 6190 6200 MJup) at a wide projected separation of 738 au (Bailey et al. Wavelength (A)˚ 2014), exterior to a debris disk that was inferred from the spectral energy distribution of the star (Chen et al. 2005). Figure 1. HARPS spectra of the HD 106906 binary system showing The inner disk was later resolved in near-infrared scattered significant changes in line morphology due to the relative velocities light as a 50 au radius ring inclined to the line of sight by of the two components. The four spectra cover a range of different ∼ orbital phases: near periapsis (φ = 0.058) where the velocity dif- 85◦ (Kalas et al. 2015; Lagrange et al. 2016). However, ∼ visible light Hubble Space Telescope (HST) data showed a ferential is highest and the lines of the two components are resolved, nine days later in the orbit (φ = 0.247) where the spectra lines are striking asymmetry in the morphology of the outer disk that the narrowest, and two subsequent phases where the shallower lines resembles the disk asymmetry of β Pic (Kalas et al. 2015). of the are being red-shifted, distorting the line profile. The The planet is oriented 21◦ from the position angle of the rest wavelengths of three calcium lines are indicated. ∼ disk midplane, suggesting that the planet’s orbit is not copla- nar with the disk (Kalas et al. 2015). HD 106906 is also a Calibrated optical spectra of HD 106906 from the High spectroscopic binary with a mass ratio near unity (Lagrange Accuracy Radial velocity Planet Searcher (HARPS; Mayor et al. 2019). et al. 2003) instrument were obtained from the European The hypothetical dynamical history of this system has been Southern Observatory (ESO) Archive (program IDs 192.C- further studied byJ ´ılkova´ & Zwart(2015), Nesvold et al. 0224, 098.C-0739, 099.C-0205) for 76 epochs from 2014 (2017), and Rodet et al.(2017). Rodet et al.(2017) quantified January to 2017 June. The radial velocities computed au- a scenario where HD 106906 b originally formed in a disk tomatically by the HARPS Data Reduction Software were near the , migrated inward, encountered an unsta- strongly biased by the blending of the rotationally broadened ble mean-motion resonance with the binary, was ejected into lines of both stars in all but four of the epochs, and were a high-eccentricity orbit, and then had its periastron raised therefore not used in the subsequent analysis. Instead, we into a stable region by an external stellar perturber. Here we use the epoch in which the lines of the two stars are the most search for potential stellar perturbers consistent with this sce- separated (2017 May 30) to fit a model atmosphere (Husser nario using the exquisite precision provided by the Gaia DR2 et al. 2013) to both stars which can then be used as a tem- astrometry and ground-based radial velocities measurements. plate to fit the Keplerian motion of both stars in the remaining epochs (Figure1). The fit was restricted to seven lines/groups 2. SYSTEMIC VELOCITY OF HD 106906 of lines centered on 5040, 5370, 5448, 5529, 6141, 6441, and ˚ 2 HD 106906 consists of a 1.37 M primary and 1.34 M 6680 A. The best-fit model was found via χ minimization by secondary with a projected separation of between 0.36– varying the temperature, surface , radial velocity and 0.58 au (Rodet et al. 2017). The full orbital characterization rotational velocity of both stars, the flux ratio, and the metal- of the system—most critically the systemic velocity—has licity. For each trial the model atmosphere was generated via not yet been published. There are four radial velocities linear interpolation, rotationally broadened, Doppler shifted, for this system within the literature, two are instantaneous and smoothed to the resolution of HARPS. The HARPS and 1 1 model atmosphere spectra were then continuum normalized (10.2 1.7 km s− , Gontcharov 2006; 15.1 0.3 km s− , ± ± Chen et al. 2011), and two are from a combination of mul- with a linear fit to the continuum. 1 The resulting template for each star was used to fit the tiple measurements (8.4 km s− , N = 22, Evans 1967; 1 Doppler shift induced by the Keplerian motion of each star 11.1 km s− , N = 2, Nordstrom¨ et al. 2004). Given the scatter in these measurements, possibly caused by the orbit over the three-year baseline. We used the affine-invariant of the binary, we opted instead to use archival spectroscopic Markov chain Monte Carlo package emcee (Foreman- observations of HD 106906 to measure the systemic velocity. Mackey et al. 2013) to fit the seven orbital elements: period ANEAR-COPLANAR STELLAR FLYBY OF THE PLANET HOST STAR HD 106906 3

P , eccentricity e, argument of periapsis ω, epoch of pe- mass. All sources within the Gaia catalog were fit with a riapsis τ, primary semi-amplitude K1, mass ratio q, and five-parameter single star model. The magnitude of this error the systemic velocity γ. At each step in the chain, the should be small given the comparable mass and flux ratio of radial velocity of both stars at each epoch was predicted the two components. from the orbital elements. The templates constructed pre- A catalog of Sco–Cen members was constructed follow- viously were Doppler shifted to the corresponding velocity, ing Wright & Mamajek(2018), augmented with members re- summed, and compared to the observed spectrum at that ported in Song et al.(2012). Astrometric measurements were epoch. Mass functions that were significantly discrepant obtained from Gaia DR2, while radial velocities came from with the apparent brightness of the system were excluded. a number of sources, either from various literature sources The period (P = 49.233 0.001 days) and eccentricity (Levato et al. 1996; Torres et al. 2006; Gontcharov 2006; ± (e = 0.669 0.002) were well constrained, and are consis- Kharchenko et al. 2007; Chen et al. 2011; Song et al. 2012; ± tent with an independent analysis by Lagrange et al.(2019). Dahm et al. 2012; Kordopatis et al. 2013; Desidera et al. 1 We found a systemic velocity of γ = 12.18 0.15 km s− 2015), or from the Gaia catalog. The final sample consisted ± after marginalizing over the remaining parameters, the er- of 461 members that had both a Gaia DR2 parallax and either ror being a combination of statistical error from the fit and a ground-based or Gaia radial velocity measurements. an assumed systematic uncertainty to account for biases in Candidate perturbers were identified through a linear ap- the fitting process estimated by repeating the fitting process proximation of the space motion of each of the sample stars using subsets of the lines described previously. relative to HD 106906. In this approximation, the velocity of each star is constant and gravitational forces are not consid- 3. CLOSE STELLAR ENCOUNTERS WITH HD 106906 ered. Uncertainties in the true position and motion of each 3.1. Identifying candidate perturbers star were propagated in a Monte Carlo fashion. A trial posi- tion, proper motion, and parallax were drawn from a multi- The revised systemic radial velocity was combined with variate normal distribution using the correlation coefficients astrometry from Gaia DR2 (Gaia Collaboration et al. 2018) in the Gaia catalog, and a radial velocity was drawn from to compute the position and kinematics of HD 106906 given a normal distribution. Closest approach times and distances in Table1. Uncertainties were propagated in a Monte Carlo (D ) were computed for each of the 105 trials. This process fashion, drawn from a multivariate normal distribution us- CA was repeated for each star within the sample. ing the correlation coefficients given in the Gaia catalog for the astrometry, and from a normal distribution for the radial velocity. One potential source of error in the Gaia astrome- 3.2. HIP 59716 and HIP 59721 try is the motion of the photocenter relative to the center of

Table 1. Kinematics for HD 106906 and two candidate perturbers

Property Unit HD 106906 HIP 59716 HIP 59721

8 8 8 α deg 184.47133075613 ± (1.48 × 10− ) 183.71107188480 ± (1.31 × 10− ) 183.71768277794 ± (1.27 × 10− ) 9 9 9 δ deg −55.97558054009 ± (7.41 × 10− ) −55.78991603504 ± (6.41 × 10− ) −55.78439084834 ± (5.86 × 10− ) π mas 9.6774 ± 0.0429 8.7068 ± 0.0393 8.6815 ± 0.0349 1 µα cos δ mas yr− −39.014 ± 0.057 −35.722 ± 0.050 −35.184 ± 0.048 1 µδ mas yr− −12.872 ± 0.046 −11.041 ± 0.042 −11.325 ± 0.039 1 a b c RV km s− 12.18 ± 0.15 15.5 ± 1.1 17.6 ± 1.7 Galactic position and motion X pc 48.54 ± 0.22 53.14 ± 0.24 53.30 ± 0.22 Y pc −90.45 ± 0.40 −100.93 ± 0.46 −101.22 ± 0.41 Z pc 11.86 ± 0.05 13.43 ± 0.06 13.48 ± 0.05 1 U km s− −9.77 ± 0.10 −8.63 ± 0.51 −7.42 ± 0.79 1 V km s− −20.12 ± 0.14 −23.09 ± 0.97 −24.83 ± 1.49 1 W km s− −7.29 ± 0.05 −6.85 ± 0.14 −6.74 ± 0.20 Galactocentric position and motion

XG pc −8251.38 ± 0.22 −8246.77 ± 0.24 −8246.61 ± 0.22

Table 1 continued 4 DE ROSA &KALAS Table 1 (continued)

Property Unit HD 106906 HIP 59716 HIP 59721

YG pc −90.45 ± 0.40 −100.93 ± 0.46 −101.22 ± 0.41

ZG pc 38.70 ± 0.05 40.26 ± 0.06 40.31 ± 0.05 1 UG km s− 1.30 ± 0.10 2.45 ± 0.51 3.66 ± 0.79 1 VG km s− 212.12 ± 0.14 209.15 ± 0.97 207.41 ± 1.49 1 WG km s− −0.01 ± 0.05 0.43 ± 0.14 0.54 ± 0.20

HD 106906 rest frame (−X0 toward Earth, Y 0 toward East, Z0 toward North)

X0 pc ··· 11.52 ± 0.69 11.85 ± 0.65

Y 0 pc · · · −0.8568 ± 0.0039 −0.8519 ± 0.0034

Z0 pc ··· 0.3675 ± 0.0017 0.3797 ± 0.0015 1 U 0 km s− ··· 3.19 ± 1.11 5.30 ± 1.71 1 V 0 km s− · · · −0.39 ± 0.13 −0.16 ± 0.13 1 W 0 km s− ··· 0.13 ± 0.06 −0.03 ± 0.06

HD 106906 debris disk frame (disk lies in YdiskZdisk plane)

Xdisk pc ··· 1.136 ± 0.061 1.179 ± 0.057

Ydisk pc · · · −0.9227 ± 0.0042 −0.9212 ± 0.0038

Zdisk pc · · · −11.46 ± 0.69 −11.79 ± 0.64 1 Udisk km s− ··· 0.30 ± 0.13 0.39 ± 0.17 1 Vdisk km s− · · · −0.41 ± 0.12 −0.15 ± 0.11 1 Wdisk km s− · · · −3.18 ± 1.10 −5.29 ± 1.70

aThis work

b Chen et al.(2011)

c Song et al.(2012)

(∆π = 0.025 0.053 mas), and the proper motion difference ± 1 Two candidate perturbers, likely forming a wide physical (0.61 0.07 mas yr− ) is less than the circular motion of a ± 1 binary, were identified as having a closest approach distance face-on 2,750 au orbit ( 1.7 mas yr− ). The similar kine- ∼ within 1 pc of HD 106906 within the last 15 Myr: HIP 59716 matics of this group of stars had been previously noted. Us- +0.90 (F5V, Houk & Cowley 1975) at tCA = 3.49 1.76 Myr, ing Hipparcos astrometry, Shaya & Olling(2010) estimated +0.93 − − DCA = 0.65 0.40 pc; and HIP 59721 (G9V, Torres et al. a probability of 92 % that HD 106906 and HIP 59716 were − +0.54 +0.18 2006) at tCA = 2.18 1.04 Myr, DCA = 0.71 0.11 pc. The bound. No assessment was made regarding the nature of HIP − − − closest approach times and distances are different for the two 59721 due to the poor quality of the parallax measurement in stars despite them likely forming a wide binary due to the the Hipparcos catalog (π = 7.56 5.84 mas, van Leeuwen ± large uncertainty on the relative radial positions and veloc- 2007). ities, and the fact that this calculation does not incorporate While the Gaia astrometry provides exquisite constraints gravitational forces (see Section 3.3). We estimate masses of on the position and motion of the two stars in the sky plane 1.37 and 1.22 M for the two stars based on their spectral (projected separation to within 0.006 au, relative motion to 1 type. The closest approach times and distances for the two within 0.008 au yr− ), the position and motion in the radial stars is shown in Figure2. These distances are comparable direction is less well constrained; the relative distance is to the closest approach of WISE J072003.20-084651.2 to the known to within 140,000 au, and the relative radial velocity +0.11 1 Sun 70 kya at 0.25 0.07 pc (Mamajek et al. 2015), although to within 0.3 au yr− . This precision is insufficient to con- the solar system is− significantly more compact than the HD firm that the two stars are bound. Instead, we make a proba- 106906 system. bilistic argument based on the chance of finding two stars in HIP 59716 and HIP 59721 are presently separated from LCC with a projected separation within 2400 that share a com- each other by 2400 on the sky and are listed in the Wash- mon parallax and proper motion. Using a simplistic assump- ington Double Star Catalog (Mason et al. 2001) as being tion that the Galactic positions and motions of LCC members a physical binary based on the similarity of their paral- within our sample follow normal distributions, we simulated lax. The Gaia DR2 astrometry is consistent with this as- 108 stars and compared their positions, parallax, and proper sessment; the parallax of the two stars are indistinguishable motions in the sky plane to that of HIP 59716. Only 20 of the ANEAR-COPLANAR STELLAR FLYBY OF THE PLANET HOST STAR HD 106906 5

2.0

1.5

(pc) 1.0 CA D

0.5

0.0

0.5

0.0 ) [pc] 0.5 CA − D 1.0 log( − 1.5 − 2.0 − 10.0 7.5 5.0 2.5 10 0 10 20 − − − − − tCA (Myr B.P.) ∆θ (deg)

Figure 2. Closest approach distance (left) and the angle between the trajectory of the flyby and the plane of the disk (right) as a function of time before present for the two candidate perturbers that had a median closest approach distance within 1 pc, HIP 59716 (red) and HIP 59721 (blue). The contours and solid histograms are from the linear approximation. Contours denote the 1σ and 2σ credible regions. For clarity, only the marginalized distributions are shown for the results of the N-body simulation (light histogram).

8 10 stars were within 2400, had a parallax within 0.078 mas, dial velocity for each star. Each simulation was integrated 1 and had total proper motion within 0.68 mas yr− , implying backwards in time, with the absolute positions and veloci- 7 a chance alignment probability of 10− . ties recorded every 100 years. The closest approach times ∼ and distances were unchanged from the linear approxima- +0.9 +0.92 3.3. N-body simulations tion tCA = 3.5 1.8 Myr, DCA = 0.63 0.39 pc for HIP − − +0.6 − +0.21 59716 and tCA = 2.2 1.0 Myr, DCA = 0.62 0.17 pc for The proximity of HD 106906 and HIP 59716 at closest ap- − − − HIP 59721 (marginalized distributions shown in Figure2). proach, and between HIP 59716 and HIP 59721 at the present The consistency between the simulations with and without epoch, motivated us to investigate the effect of the gravita- gravity was expected. The difference in the Galactic potential tional interaction between the stars and the influence of the experienced by the three stars over a small fraction of their Galactic potential. We used the N-body REBOUND pack- Galactic orbital period is negligible, and the large uncertainty age (Rein & Liu 2012; Rein & Spiegel 2015) to predict the on the relative radial velocity and distance between HIP position of the three stars within a Galactic potential (Bovy 59716 and HIP 59721 meant that the pair were only bound 2015) over the previous 10 Myr. We initialized 104 simula- in 2 % of the simulations. The closest approach distances tions to sample the uncertainties on the astrometry and ra- ∼ 6 DE ROSA &KALAS

the plane of the disk is rotated 15◦ about the X0 axis and 85◦ about the Y 0 axis. The second is rotated about the first such 1.0 that the disk lies in one of the planes of the coordinate system (Y Z ). A schematic diagram is shown in Figure4. 0.5 disk disk

(pc) The trajectories of both stars were almost coplanar with the +1.5 0.0 current plane of the debris disk: ∆θ = 5◦.4 1◦.7 (5◦.2 ) disk 1.8

Z +0.9 ± − for HIP 59716 and ∆θ = 4◦.2 (4◦.8 1◦.0) for HIP 59721

∆ 0.5 1.1 − ± − (Fig.1, second column; values in parentheses were calcu- 1.0 − lated from the N-body simulation). The relative inclination 1.0 between the flyby and the orbit of the planet cannot be con- 0.5 strained due to the lack of multi-epoch astrometry to mea-

(pc) sure the planets orbit. We calculated a relative velocity of 0.0 1 1

disk 3.3 1.1 km s− and 5.3 1.7 km s− at the time of closest

Y ± ±

∆ 0.5 approach in the N-body simulation for HIP 59716 and HIP − 59721, respectively. The velocity vector is almost entirely in 1.0 − the disk plane, consistent with a coplanar encounter. 1.0 0.5 0.0 0.5 1.0 1.0 0.5 0.0 0.5 1.0 − − − − ∆Xdisk (pc) ∆Zdisk (pc)

Figure 3. Closest approach locations of HIP 59716 (red) and HIP 4. EFFECT OF MEASUREMENT UNCERTAINTIES 59721 (blue) relative to HD 106906 (black star) from the linear ap- The relative three-dimensional motion between HD proximation in the coordinate system defined by the HD 106906 106906 and the two candidate perturbers is almost entirely disk. The correlation between pairs of coordinates are shown, as well as marginalized distributions. The cross indicates the location in the radial direction, and as such our uncertainty on the of the 50th percentile in the marginalized distributions; the size of closest approach distance is almost entirely due to the uncer- the symbol is arbitrary. Solid contours denote 1 and 2-σ credible tainty in the relative radial positions and motions of the three regions. The corresponding marginalized distributions from the N- stars. While the uncertainty in the relative radial positions body simulation of the three stars are also plotted (light histograms). of the three stars is a factor of 108 larger than the relative tangential positions, the dominant source of uncertainty on were not significantly different for the bound simulations, in- the predicted closest approach distance is the relative radial +0.30 creasing slightly for HIP 59716 to DCA = 0.42 0.17 pc, and velocity as this error accumulates as the positions of each − +0.30 decreasing slightly for HIP 59721 to DCA = 0.42 0.18 pc. star are traced back in time. We note that these values are derived from a small− number To explore the effects of varying the relative radial ve- of simulations (212 of 10,000), and may not constitute a rep- locities on the closest approach differences, we repeated the resentative sample of bound orbit trajectories. The projected traceback analysis for HIP 59716 and HIP 59721 for a range separation between the two stars of 2,750 au suggests a com- of plausible radial velocities. For each combination of ra- parable semi-major axis with the a/ρ conversion factor peak- dial velocities, we drew 104 random variates from the mul- ing at unity for a uniform eccentricity distribution (Dupuy & tivariate normal distribution that describe the Gaia astrom- Liu 2011). Only in the most extreme cases where a/ρ 3 etry and their correlation for each star and determined D ∼ CA and e 1 does the apocenter distance, where eccentric bi- and t using the linear approximation described previously. ∼ CA naries spend more of their time, become comparable to the We assume that the radial velocities are perfectly measured. closest approach distance. For the purposes of this study, we The correlations between DCA and tCA and the radial ve- assume that the dynamics of the binary system—if it is in- locities of the three stars are shown in Figure5. DCA and deed bound—does not have a large effect on the flyby of HD tCA are only sensitive to the relative radial velocity between 106906. HD 106906 and the two other stars rather than their abso- lute velocities; lines of constant DCA and tCA follow lines 3.4. Flyby geometry of constant relative velocity. Increasing the relative velocity The position and motion for the three stars in the Galac- between HD 106906 and HIP 59716 causes a significant de- tic and Galactocentric coordinate systems are given in Ta- crease in DCA and an increase in tCA (a more recent flyby). ble1. We defined two new coordinate systems with HD Interestingly, if HIP 59716s radial velocity was similar to that 106906 at the origin (in terms of both position and veloc- of HIP 59721, the median value of DCA would be near the ity). The first has X0 pointing toward the current location global minimum found in this grid search. HIP 59716 and − of the Sun and Y 0 and Z0 pointing toward East and North HIP 59721 both have relatively large uncertainties on their from the perspective of the Sun. In this coordinate system, radial velocities, and periodic measurements will be required ANEAR-COPLANAR STELLAR FLYBY OF THE PLANET HOST STAR HD 106906 7

1.0

Xdisk 0.5 1.0 Z0 (North) Xdisk Z0 (North) 0.5 X0

[pc] Y 0 (East) [pc]

0 0.0 0.0 0 Ydisk Y 0 (East) Z Zdisk Z Ydisk to Earth 0.5 − 0.5 1.0 − − 1.0 1.0 − 0.5 0.5 1.0 − − X 0.0 0.0 0 [pc] [pc] 0.5 0.5 0 1.0 0.5 0.0 0.5 1.0 − Y − − 1.0 1.0 Y 0 [pc] − Figure 4. Schematic of the close encounter between HD 106906, HIP 59716 (red tracks), and HIP 59721 (blue tracks) in the rest frame of HD 106906. The left panel shows the flyby as viewed from the Sun’s current position relative to HD 106906, and the right panel is rotated 45◦ in both azimuth and elevation. In both panels the sky plane (Y 0Z0) is denoted by a gray plane, and the disk plane (YdiskZdisk) by a blue plane. The location of closest approach for each trajectory is marked by a point connected to the origin with a gray line. Both stars approach HD 106906 from the −X0 direction, moving almost entirely in the X0Y 0 plane.

22 1.20 in order to rule out the presence of binary companion to ei- 0.25 pc 0.50 pc ther of the two stars. ) 1

− 20 -3 Myr 1.00 -1 Myr -2 Myr 5. MAGNITUDE OF DYNAMICAL INTERACTION (pc) (km s 18 0.80 There are two peculiar features of the HD 106906 system CA -5 Myr that may be explained by the dynamical perturbation caused 16 0.50 pc 0.60 D -4 Myr by a passing star: the asymmetric debris disk (Kalas et al. HIP59716

γ -4 Myr 2015; Lagrange et al. 2016) and the planet at a large pro- 14 0.75 pc 0.40 -5 Myr jected separation (Bailey et al. 2014). The debris disk has two components: an inner ring at a radius of 50 au that ex- 22 1.20 hibits a strong brightness asymmetry, and a sharp feature re-

) solved with HST extending at least 500 au westward along the

1 1.10

− 20 -1 Myr 1.00 disk plane with no counterpart seen on the eastern side (Kalas 0.75-5 Myr pc et al. 2015). Several theories have been suggested to explain -2 Myr (pc) (km s 18 0.90 the observed asymmetry including perturbation by the planet 0.80 CA 16 D on its current orbit (J´ılkova´ & Zwart 2015; Nesvold et al. -4 Myr

HIP59721 -3 Myr 0.70 2017), and a scattering event where the planet interacted with γ 14 0.60 either an unseen low-mass companion (Kalas et al. 2015) 0.50 or the inner binary (Rodet et al. 2017) and then migrated 8 10 12 14 16 through the disk. The presence of the planet at a projected 1 γHD106906 (km s− ) separation of 738 au is also a mystery. Canonical planet for- mation theories suggest that massive planets cannot form at D Figure 5. Correlation between CA (color scale, dashed contours), such wide separations. Instead, the planet must have either tCA (solid contours), and the relative velocities of HD 106906, HIP 59716 (top panel), and HIP 59721 (bottom panel). The radial ve- formed closer in and later migrated or was scattered to its locities used in this study are indicated with error bars denoting 1-σ current separation, or formed more like a binary star in the uncertainties. The color scales for each plot have been normalized initial fragmentation of the molecular cloud as HD 106906 to the range of DCA values for each star. itself was being formed. The flyby of HIP 59716 and HIP 59721 may have been important in the context of both the observed asymmetry in the debris disk and the current wide separation of the planet. 8 DE ROSA &KALAS

The two stars passed well within the tidal radius of the HD 0.9999 3 106906 binary (1.9 pc; Jiang & Tremaine 2010; Mamajek 10 et al. 2013) interior to which the gravitational interaction be- tween the stars is stronger than the Galactic potential. In a 102 recent study, Rodet et al.(2017) postulated that the present orbit of the planet could be explained by a combination of (au) e dynamical interaction with an eccentric inner binary (we find 1 0.999 peri 10 r e 0.67 based on our orbit fit discussed previously) and a ∆ ∼ close encounter with a passing star.

In this scenario, the planet formed at a location within the 100 circumbinary disk that was stable to the dynamical effects of the binary. After formation, the planet migrated inward until 1 it was temporarily trapped in a 1:6 mean-motion resonance 10− 2 1 0 0.99 10− 10− 10 with the inner binary. Dynamical interaction with the inner DCA (pc) binary cause the semi-major axis of the planet to rapidly os- cillate before being ejected from the inner system. Rodet Figure 6. The correlation between the change in periapsis distance et al.(2017) suggests that the very eccentric (or hyperbolic) (∆rperi) of an orbiting planet as a function of closest approach dis- orbit of the ejected planet could then be stabilized by an in- tance (DCA) for the 21,651 prograde (filled symbols) and 6,435 ret- rograde (open symbols) N-body flyby simulations that resulted in a teraction with a passing star that decreases the eccentricity of significant increase of rperi for the planet. The symbols are coloured the orbit and raises the periapsis distance out of the chaotic on a logarithmic scale according to the eccentricity of the planet at zone surrounding the binary. Without a stabilizing encounter the start of the simulation. the planet would enter the chaotic zone surrounding the inner binary each time it goes through periapsis, rapidly leading to For the older age estimate of 20 Myr, the planet would ∼ the complete ejection of the planet from the system. need to spend over ten million years outside of the chaotic The configuration of the flyby required to increase the pe- zone surrounding the binary before entering the mean-motion riapsis distance out of the chaotic zone depends on the mass resonance approximately four million years ago. These tim- and closest approach distance of the passing star, the incli- ings are inconsistent with the requirement of a massive cir- nation of the encounter, and the angle between the velocity cumstellar disk to enable planetary migration; disks around vector of the planet and passing star. Such a scenario has also the majority of young stars dissipate within a few million been suggested for the hypothesized ninth planet within our years (e.g., Ansdell et al. 2017). In this case, if a stabiliz- own solar system (Batygin & Brown 2016), with the planet ing encounter did occur, it is more likely to have been with being ejected from the inner solar system due to interactions another cluster member in the more distant past, rather than with the other gas giants, and then stabilized by the gravita- with HIP 59716 and HIP 59721. Future work could search tional influence of a passing star (Bromley & Kenyon 2016). for a dynamical process where the ejection of HD 106906 b In the scenario described by Rodet et al.(2017), the planet occurs at a later epoch than calculated by Rodet et al.(2017). is rapidly ejected from the inner system after reaching the 1:6 mean-motion resonance with the inner eccentric binary. The 5.1. Flyby simulations window for a stabilizing timescale is short (<104 yr); either We ran 5 104 REBOUND N-body simulations to explore the planet is ejected immediately on a hyperbolic trajectory, × the dynamical impact of a stellar flyby on a planet with a or it first achieves a highly eccentric orbit that evolves into a highly eccentric ( ) orbit. For these simulations we hyperbolic trajectory after a few passes through the chaotic e > 0.9 assumed that HIP 59716 and HIP 59721 form a physical bi- zone surrounding the binary. Given a mean age of 15 Myr nary, and treated them as a single particle of their combined for LCC members, and an intrinsic scatter of 6 Myr (Pecaut mass given current uncertainties about their orbit. This is a & Mamajek 2016), the plausible ages for HD 106906 range reasonable approximation when the flyby distance is signif- from 9–21 Myr. Assuming a younger age of 10 Myr, the ∼ icantly larger than the binary separation, where the gravita- formation of the planet and migration into mean-motion res- tional influence of the two stars would not be resolved by onance with the inner binary has to occur in 5 Myr for the ∼ the orbiting planet, but may not be valid in cases where the planet to be ejected as the perturbing stars were passing by. minimum separation between the planet and perturbing stars These timescales are similar to those proposed for planet for- is comparable to their orbital semi-major axis. We note that mation via pebble accretion (e.g., Lambrechts & Johansen these simulations do not model the ejection mechanism it- 2014), although formation via gravitational instability would self, rather the planet is initialized on a highly eccentric orbit occur much more rapidly (e.g., Boss 2011). to simulate the orbital configuration after an ejection has oc- ANEAR-COPLANAR STELLAR FLYBY OF THE PLANET HOST STAR HD 106906 9 curred. A more detailed modeling effort will be needed to important close encounter with HD 106906 within the last combine an ejection event with a stellar flyby into a single 15 Myr. The flyby of these two stars fulfill many of the cri- simulation. teria for the stabilization scenario described in Rodet et al. Each simulation was initialized with a 2.71 M parti- (2017). Their trajectories are almost coplanar with the de- cle at (0, 0) pc, accounting for the combined mass of the bris disk in its current orientation, their velocities relative to HD 106906 binary, around which a 11 MJup particle was HD 106906 at closest approach are low (the change in veloc- placed with an orbital eccentricity of log (1 e) drawn ity of the orbiting planet being inversely proportional to the 10 − from ( 4, 1) (where denotes the uniform distribu- relative velocity of the passing star at closest approach), and U − − U tion), a semi-major axis with a corresponding periapsis dis- the distribution of closest approach distances for HIP 59716 tance (rperi) of 1.5 au, and a mean anomaly M drawn from is consistent with a dynamically significant encounter within (0, 2π) rad so that the flyby occurs at a different phase of 0.5 pc. U the orbit within each simulation. The two candidate per- The biggest source of uncertainty in the closest approach turbers were modeled by a single particle with a mass of distances are the relative radial velocities. Future spec-

2.59 M , initialized at y = 3 pc, log10(x) drawn from troscopic observations of the two candidate perturbers will − 1 ( 2, 0.5) pc, with a velocity of dy/dt = 3 km s− . In be essential to precisely determine their radial velocities. U − half of the simulations the perturber was instead initialized For example, increasing the relative velocity between HD 1 1 at y = 3 pc, with a velocity of dy/dt = 3 km s− , to ac- 106906 and HIP 59716 by 1 km s− significantly increases − count for the unknown direction of the orbit of the planet. A the probability of a closest approach distance within 0.1 pc coplanar encounter was assumed to limit the size of phase (Fig.5). The astrometry for each star will also be improved space to explore. Each simulation was advanced either until with upcoming Gaia data releases. Not only will the preci- the perturbers had reached y = 3 pc (or 3 pc), or for 2 Myr, sion of the measurements improve, but the photocenter mo- − whichever occurred first. tion of short period binaries will also be accounted for. With Of the 25,000 prograde (retrograde) flybys; 21,670 (6,385) these data in hand, a more precise determination of the kine- caused an increase in rperi and 3,330 (18,615) led to a de- matics of the three stars can be made. crease in rperi, with 1,541 (1,525) resulting in the planet be- ing ejected from the system. The correlation between the We wish to thank Eric Nielsen, Ian Czekala, Ruth Murray- change in periapsis distance (∆rperi) and the closest ap- proach distance between the two stars for the simulations in Clay, and Anne-Marie Lagrange for useful discussions relat- which the eccentricity decreased is shown in Figure6. There ing to this work. We also wish to thank the referee for the comments that helped improve the quality of this work. The is a clear correlation between ∆rperi and DCA, with closer authors were supported in part by NSF AST-1518332, NASA encounters leading to a larger ∆rperi for a given initial eccen- tricity. The presence of a debris ring at 50 au around the HD NNX15AC89G and NNX15AD95G. This work benefited ∼ from NASA’s Nexus for Exoplanet System Science (NExSS) 106906 binary suggests that the rperi for the planet is now > 50 au, otherwise the disk would be disrupted with each research coordination network sponsored by NASAs Sci- ence Mission Directorate. This work has made use of periastron passage for relative inclinations . 10 deg (J´ılkova´ & Zwart 2015). Periapsis distances interior to the radius of data from the European Space Agency (ESA) mission Gaia the debris ring are possible for higher relative inclinations (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC; https: (& 40 deg) without disrupting the disk. These N-body simu- //www.cosmos.esa.int/web/gaia/dpac/consortium). Funding lations suggest that rperi for a highly eccentric planet can be plausibly raised from 1.5 to 100 au with a co-planar stel- for the DPAC has been provided by national institutions, in ∼ ∼ lar flyby within 0.2 pc. Future observational and theoretical particular the institutions participating in the Gaia Multilat- work is needed to more precisely constrain the geometry of eral Agreement. This research has made use of the SIMBAD the encounter and its dynamical consequences. database and the VizieR catalog access tool, both operated at the CDS, Strasbourg, France. 6. CONCLUSIONS Software: Astropy (The Astropy Collaboration et al. HIP 59716 and HIP 59721 are the best candidates of the 2013), Matplotlib (Hunter 2007), galpy (Bovy 2015), RE- currently known members of Sco–Cen for a dynamically BOUND (Rein & Liu 2012)

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